Host–pathogen time series data in wildlife support a transmission function between density and frequency dependence

Abstract

A key aim in epidemiology is to understand how pathogens spread within their host populations. Central to this is an elucidation of a pathogen's transmission dynamics. Mathematical models have generally assumed that either contact rate between hosts is linearly related to host density (density-dependent) or that contact rate is independent of density (frequency-dependent), but attempts to confirm either these or alternative transmission functions have been rare. Here, we fit infection equations to 6 years of data on cowpox virus infection (a zoonotic pathogen) for 4 natural populations to investigate which of these transmission functions is best supported by the data. We utilize a simple reformulation of the traditional transmission equations that greatly aids the estimation of the relationship between density and host contact rate. Our results provide support for an infection rate that is a saturating function of host density. Moreover, we find strong support for seasonality in both the transmission coefficient and the relationship between host contact rate and host density, probably reflecting seasonal variations in social behavior and/or host susceptibility to infection. We find, too, that the identification of an appropriate loss term is a key component in inferring the transmission mechanism. Our study illustrates how time series data of the hostpathogen dynamics, especially of the number of susceptible individuals, can greatly facilitate the fitting of mechanistic disease models.cowpox ͉ disease ͉ population cycles ͉ Markov chain Monte Carlo T he seminal studies of Anderson and May (1, 2) introduced a framework for modeling the dynamics of pathogens and their hosts that has since underpinned most predictive models of host-pathogen dynamics. It has been standard practice when modeling the dynamics of host-microparasite interactions (viral and bacterial infections) to represent the rate of change of infected hosts I(t) at time t by dI͑t͒ dt ϭ transmission rate ͑infection͒ Ϫ loss rate ͑death ϩ recovery͒.[1]However, empirically based identification of appropriate functional forms for the ''transmission rate'' and ''loss rate'' terms has not generally been possible for systems with host dynamics because of a lack of sufficient data (although refs. 3 and 4 have recently done this for infectious diseases of human populations).To date, most studies have used transmission rate terms that are either density-dependent or frequency-dependent (5, 6). The underlying difference between these is the assumption about how host contact rate c, varies with host density [(N(t))/A], where N(t) is host abundance and A, the area occupied by the population, is usually assumed constant and omitted from the equations (6). For density-dependent transmission, host contact rate varies linearly with density [typically adopted for directly transmitted diseases such as measles (7) and foot and mouth disease (8)], whereas for frequencydependent transmission it is constant [typically adopted for sexually transmitted diseases such as HIV in ...

Deer density and disease prevalence influence transmission of chronic wasting disease in white‐tailed deer

“…At low deer density (e.g., ,5-10 deer/mi 2 ), disease transmission increases in a density-dependent manner until it reaches a saturation (or frequency-dependent) level. Disease transmission as a saturating function of density has been suggested as an alternative to linear density-and frequencydependence (Antonovics et al 1995, Roberts 1996, and has empirical support from other systems (Cross et al 2009, Smith et al 2009, Habib et al 2011. Our findings support the notion that classic frequency-and density-dependent models inadequately represent disease transmission processes in hosts with complex social behavior.…”

“…When disease transmission rates are independent of density (frequency-dependent), host-pathogen coexistence is uncertain and generalized culling is unlikely to be successful, because transmission, and hence, disease-induced mortality, is maintained at low host densities (Getz and Pickering 1983, de Castro and Bolker 2005, McCallum et al 2009). While frequency-and density-dependent transmission have received the bulk of attention, they represent opposite extremes, and intermediate forms of transmission may be more realistic for natural systems (Barlow 2000, McCallum et al 2001, Schauber and Woolf 2003, Smith et al 2009). Knowledge of the correct transmission function is essential to properly forecasting disease-host dynamics and devising appropriate management strategies.…”

Host density thresholds and disease control for fisheries and aquaculture

“…This is because a pathogen, either in an infected individual or free-living in the environment, has a greater chance of encountering a new host individual if there are a greater number of hosts in the immediate environment. Such density-dependent transmission is common in host -parasite dynamics (May & Anderson 1991, Hudson et al 2001, although there are exceptions (McCallum et al 2001, Wonham et al 2006, Smith et al 2009). Density-independent transmission in terrestrial environments typically involves vector or sexually transmitted diseases; these are rarer in aquatic environments.…”

A multi‐scale assessment of animal aggregation patterns to understand increasing pathogen seroprevalence

“…These results suggest that patterns of aggregation related to both within-and between-group transmission may be increasing the spread of B. abortus among elk. Such complex transmission mechanisms may occur, for example, in animals with distinct social groups that are highly connected due to group-group contact and between-group movement of certain individuals (e.g., Craft et al 2011), and may explain wildlife systems where the prevalence of disease is not described well by a linear relationship with host density (e.g., Smith et al 2009, Storm et al 2013. However, few studies have evaluated and compared the effects of density and group size measured at multiple scales or examined the relationship between density of a large mammal and rate of increase in pathogen seroprevalence.…”

“…However, such data are rare for large mammals where extensive datasets on disease prevalence and animal aggregations are difficult to obtain. In particular, studies of density and transmission may rely on temporal variation in parasite prevalence and density (Begon et al 1999, Ostfeld et al 2001, Smith et al 2009), but few datasets will be long enough to conduct this type of analysis for a long-lived animal and chronic disease. Instead, we focused on the spatial variation in serologic data and elk (Cervus canadensis) aggregation measured at multiple scales across 10 regions in western Wyoming and the Greater Yellowstone Area (GYA) where elk have been exposed to Brucella abortus, a bacteria that causes brucellosis.…”